Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Embedding of a Banach algebra $A$ into $L(A')$

Author: Etienne Desquith
Journal: Proc. Amer. Math. Soc. 124 (1996), 2773-2778
MSC (1991): Primary 46H15
MathSciNet review: 1327005
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a Banach space $X$, we have shown in 1994 that a product can be defined on it in such a way that the resulting Banach algebra is isomorphic to a compact subalgebra of the algebra $L(X')$ of all bounded linear operators on the topological dual $X'$ of $X$. Our purpose here is to prove that, more generally, any Banach algebra $A$ admitting a left approximate identity, is isomorphic to a subalgebra of $L(A')$, the isomorphism being isometric, provided the approximate identity is bounded by 1. As a consequence, we get a factorization through $L(A')$, of the elements in $A'$.

References [Enhancements On Off] (What's this?)

  • 1. Frank F. Bonsall and John Duncan, Complete normed algebras, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80. MR 0423029
  • 2. E. Desquith, Structures d'algèbre de Banach sur le dual topologique d'un espace de Banach et applications, Thèse de Doctorat D'Etat, Université d'Abidjan (FAST), 1992.
  • 3. Etienne Desquith, Sur quelques propriétés de certaines algèbres dont tout sous-espace vectoriel est an ideal, Algebras Groups Geom. 11 (1994), no. 3, 309–327 (French, with French summary). MR 1307676
  • 4. Jacques Dixmier, Les 𝐶*-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
  • 5. Lawrence Narici and Edward Beckenstein, Topological vector spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 95, Marcel Dekker, Inc., New York, 1985. MR 812056

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46H15

Retrieve articles in all journals with MSC (1991): 46H15

Additional Information

Etienne Desquith
Affiliation: Institut de Recherches Mathématiques (IRMA), 08 BP 2030 Abidjan 08, Cote D’Ivoire

Received by editor(s): September 29, 1994
Received by editor(s) in revised form: March 13, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society